Semiparametric tests for equality of two independent variances

In this article, we propose new semiparametric and bootstrap tests based on the ratio of two variances under a density ratio model and compare them with existing tests for testing the equality of two variances from two independent populations. We showed that the ratio of two independent variances follows an asymptotic log-normal distribution. Also presented in this article are large sample asymptotic results of the semiparametric estimator of the ratio of the two sample variances. We also present a theoretical comparison of our semiparametric test on the ratio of two variances with the existing non parametric test using Pitman's relative efficiency. Numerical comparisons of the performance of various tests are performed via simulation studies. We also use two numerical examples to illustrate the implementation of new tests.